I kept a chameleon in a bird cage for a while, temporarily of course. The results were actually fine. He was a run away that I finally found in my expansive back yard... amongst maybe 300 orchids that my grandmother hand grows.
I had gotten rid of all his previous needs, so the birdcage was a last minute use.
However, with a bird cage there are a lot of things to consider:
1. How far is the spacing between bars compared to the size of the chameleon? Always ensure that they are spaced smaller than the animals head. He can't go anywhere if the head can not follow.
2. Will he be kept indoors or outdoors? Outdoors and bird cages allow the high probability that insects will invade the cage, attracted to the mist/plants/lights. This potentially brings contaminated material into the enclosure, such as fly eggs, bacteria - even the possibility that your chameleon will eat an insect that has been in areas sprayed with pesticides or fertilizers. On the opposite hand, food the chameleon should be eating, may also escape.
A solution would be if you are keeping the enclosure outdoors to wrap it with thin mesh, which you can pick up cheaply at home depot. Wrap the mesh around the entire cage and secure it well.
3. If the cage is indoors, I would still consider wrapping it in the mesh.
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As Pssh said before, it is better to have a setup and no chameleon than a chameleon and no setup. Chameleons are not like other animals, mistakes in husbandry can often lead to the death of the animal, or a costly vet visit.
Please consider, that if you are buying this animal from a generic pet store - petco for example, that you are not going to be getting a very high quality pet. These animals are usually sold to petco by breeders for pennies on the dollar, and the animals treatment reflects on that. Like you said, they were being kept in a glass enclosure with a screen top - thats already a bad sign.
Go back to the pet store and snoop a bit
things to look for:
Does their enclosure have an obvious basking spot? if you can't see it - the cham probably does not have one.
Does the enclosure have a
Suitable UVB source?
What are they feeding the chameleons? are these gut loaded?
How are the animals hydrated?
I can tell you for a fact that my local petco,
does:
Not use a basking spot.
Not use a UVB source
Not gutload
MAYBE mists once a day - water bowl provided of course

DOES - keep animals past 5 months of age in the same enclosure ( this is a no no ) ive seen juveniles in the same cage with neonates.....
DOES feed the chameleons a diet consisting of meal worms... and mealworms
DOES keep these chameleons in a glass case
Please compare this list to what you see in the pet shop you are considering purchasing from.
This improper husbandry will usually ensure that your purchase will never be as healthy/happy/strong as it could have been. It can also mean expensive trips to a specialized veterinarian, and premature death of the animal.
To top it all off, these pet stores will usually charge you two to three times the actual cost of the animal.
Please, before purchasing an animal that comes from these conditions - consider that you can purchase one at less than half the cost, and much much healthier.
Examples of people I have gotten chameleons from before, and of course the animals turned out excellent.
1.
http://flchams.com/
2.
http://chameleonsnorthwest.com/
3.
http://tikitikireptiles.com/
Before purchasing any chameleon make sure that you have the proper setup. Too many people keep these poor animals in aquariums and then wonder why the cham was dead in two months - Its unfair to the animal.
Consider purchasing this first
http://lllreptile.com/store/catalog...-cage-packages/-/38-gallon-chameleon-package/
It is a more than decent starter setup for the animal, and the price is great.
Or even this, everything you need to get started - including a healthy animal to start with.
http://lllreptile.com/store/catalog/animals/chameleons/-/veiled-chameleon-package/
Or you can purchase everything separately and go with higher quality products. I even made you a sample purchase
http://lllreptile.com/store/cart
This would be a great start and the products are of superior quality - they will last the chameleons entire lifetime. Except the enclosure, which will probably need to be replaced with a larger one.
I hope this helps,
S.F
Edit:
The cart shows it contents on my screen, however this may not be true on yours.
Product Qty Total
18 x 18 x 36 inch Aluminum Screen Cage
$57.00 each
Screen Cage Trim Color: Grey
$57.00
Zoo Med 18" Repti Sun 5.0 UVB bulb
$17.99 each
$17.99
Exo Terra Jungle Vine Small
$5.99 each
$17.97 - this is for three
8 1/2" Aluminum Ceramic Fixture
$9.50 each
$9.50
2-Pack Zoo Med 50 Watt Basking Bulbs
$10.99 each
$10.99
72 Inch tropical vine
$3.99 each
$7.98 - for two.
20" fluorescent hood fixture
$26.99 each
$26.99
$26.99
Subtotal $121.43
Tax TBD
Shipping $16.95
Total $174.87